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**A goal programming procedure for fuzzy multiobjective linear fractional programming problem.**
*(English)*
Zbl 1047.90081

Summary: This paper presents a goal programming (GP) procedure for fuzzy multiobjective linear fractional programming (FMOLFP) problems.

In the proposed approach, which is motivated by R. H. Mohamed [Fuzzy Sets Syst. 89, 215–222 (1997)], GP model for achievement of the highest membership value of each of fuzzy goals defined for the fractional objectives is formulated. In the solution process, the method of variable change on the under- and over- deviational variables of the membership goals associated with the fuzzy goals of the model is introduced to solve the problem efficiently by using linear goal programming (LGP) methodology. The approach is illustrated by two numerical examples.

In the proposed approach, which is motivated by R. H. Mohamed [Fuzzy Sets Syst. 89, 215–222 (1997)], GP model for achievement of the highest membership value of each of fuzzy goals defined for the fractional objectives is formulated. In the solution process, the method of variable change on the under- and over- deviational variables of the membership goals associated with the fuzzy goals of the model is introduced to solve the problem efficiently by using linear goal programming (LGP) methodology. The approach is illustrated by two numerical examples.

### MSC:

90C70 | Fuzzy and other nonstochastic uncertainty mathematical programming |

90C29 | Multi-objective and goal programming |

90C32 | Fractional programming |

### Keywords:

Multiobjective linear fractional programming; Fuzzy multiobjective linear; fractional programming; Fuzzy programming; Fuzzy goal programming; Goal programming; Linear goal programming
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\textit{B. B. Pal} et al., Fuzzy Sets Syst. 139, No. 2, 395--405 (2003; Zbl 1047.90081)

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